ION Audio vinyl to MP3 converter.

I recommend an ION turntable. These hook up to your computer via a USB cable, and come with software to convert your vinyl records to MP3s. I have one for cassette tapes, and it works very well. The only thing is you have to play each disk at it's normal speed, turn it over, etc., so the process can be tedious. They have many different models. Check out http://www.ionaudio.com/products/audio-conversion.

By the way, if you're willing to buy CDs, have you checked on iTunes to see if the albums are available? This would be much more expensive in the long run, but also much faster and easier.